Approximation to Constant Functions by Electrostatic Fields due to Electrons and Positrons
- Authors: Komarov M.A.1
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Affiliations:
- Department of Functional Analysis and Its Applications
- Issue: Vol 40, No 1 (2019)
- Pages: 79-84
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203796
- DOI: https://doi.org/10.1134/S1995080219010104
- ID: 203796
Cite item
Abstract
We study a uniform approximation to constant functions f(z) = const on compact subsets K of complex plane by logarithmic derivatives of rational functions with free poles. This problem can be treated in terms of electrostatics: we construct on K the constant electrostatic field due to electrons and positrons at points ∉ K. If K is a disk or an interval, we get the approximation, which close to the best. Also we get the new identity for generalized Laguerre polynomials. Our results related to the classical problem of rational approximation to the exponential function.
About the authors
M. A. Komarov
Department of Functional Analysis and Its Applications
Author for correspondence.
Email: kami9@yandex.ru
Russian Federation, Vladimir, 600000